Q. Afflux on account of obstruction to flow?
Even if the river constriction on account of approach banks is not excessive and bridge waterway is wider than that causing critical discharge intensity, afflux can still be generated due to obstruction to flow by piers. Separation eddies forming at such obstructions result in loss of head which shows as afflux upstream of the bridge.
h = [(V2 / 17.88) + 0.01524] [(A/a)2-1]
wherein h is afflux in m, V is velocity in m/s in unobstructed stream, A is unobstructed sectional area of the river in m2 and a is obstructed sectional area of the river in m2. Other formulae in wide use are due to Negler and Yarnell.
More recently, the Bureau of Public Roads U.S.A., have adopted procedure for estimation of afflux detailed in Hydraulics of Bridge Waterway.